First-principles study on magneto-optical effects in the ferromagnetic semiconductors Y3Fe5O12 and Bi3Fe5O12

The magneto-optical (MO) effects are a powerful probe of magnetism and electronic structure of magnetic solids but also have valuable applications in high-density data-storage technology. Yttrium iron garnet (${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$) (YIG) and bismuth iron garnet (${\mathrm{Bi}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$) (BIG) are two widely used magnetic semiconductors with significant magneto-optical effects. In this paper, we present a thorough theoretical investigation on magnetism, electronic, optical, and MO properties of YIG and BIG, based on the density functional theory with the generalized gradient approximation plus on-site Coulomb repulsion. We find that YIG exhibits significant MO Kerr and Faraday effects in UV frequency range that are comparable to ferromagnetic iron. Moreover, BIG shows gigantic MO effects in visible frequency region that are several times larger than YIG. This is because the calculated MO conductivity (${\ensuremath{\sigma}}_{xy}$) of BIG is nearly ten times larger than that of YIG. Interestingly, the calculated band structures reveal that BIG is a single spin semiconductor. They also show that in YIG, Y $sd$ orbitals mix mainly with the high-lying conduction bands, leaving Fe $d$ orbital dominated lower conduction bands almost unaffected by the spin-orbit coupling (SOC) on the Y atom. In contrast, Bi $p$ orbitals in BIG hybridize significantly with Fe $d$ orbitals in the lower conduction bands, leading to large SOC-induced band splitting in the bands. Consequently, the MO transitions between the upper valence bands and lower conduction bands are greatly enhanced when Y is replaced by heavier Bi. Our calculated Kerr and Faraday rotation angles of YIG as well as Faraday rotation angles for BIG agree well with the available experimental values. Thus, we believe that our predicted giant MO Kerr effect in BIG will stimulate further MOKE experiments on high-quality BIG crystals. This work thus shows that the iron garnets not only offer a useful platform for exploring the interplay of spin current, magnetism, and optics degrees of freedom, but also have promising applications in high-density MO data-storage and low-power consumption spintronic nanodevices.